Geodesic
Dihedral Angles of 4-Ball Tetrahedra
Journal for geometry and graphics, Tome 25 (2021) no. 2, pp. 197-204 Cet article a éte moissonné depuis la source Heldermann Verlag

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A tetrahedron is a 4-ball tetrahedron if there are four externally tangent spheres centered at the vertices of the tetrahedron. It is known that a tetrahedron being a 4-ball tetrahedron is equivalent to (1) three pairs of the sum of opposing edge lengths are the same, and to (2) there is a sphere tangent to each edge of the tetrahedron. We will prove that a tetrahedron is a 4-ball tetrahedron if, and only if three pairs of the sums of opposing dihedral angles are the same.
Classification : 51M15, 51M04
Mots-clés : Four-ball tetrahedron, balloon tetrahedron, edge-additive tetrahedron, edge-tangent sphere, circumscriptable tetrahedron, edge-incentric tetrahedron, dihedral-angle-additive tetrahedron 
@article{JGG_2021_25_2_JGG_2021_25_2_a3,
     author = {H. Katsuura },
     title = {Dihedral {Angles} of {4-Ball} {Tetrahedra}},
     journal = {Journal for geometry and graphics},
     pages = {197--204},
     year = {2021},
     volume = {25},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JGG_2021_25_2_JGG_2021_25_2_a3/}
}
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H. Katsuura . Dihedral Angles of 4-Ball Tetrahedra. Journal for geometry and graphics, Tome 25 (2021) no. 2, pp. 197-204. http://geodesic.mathdoc.fr/item/JGG_2021_25_2_JGG_2021_25_2_a3/